Related papers: Massey products and configuration spaces
We present two models for the space of knots which have endpoints at fixed boundary points in a manifold with boundary, one model defined as an inverse limit of spaces of maps between configuration spaces and another which is cosimplicial.…
A cohomological study is made of an equivariant map betwen the configuration space of n points in space and the flag manifold of U(n).
We study the relation between the persistent homology and the spectral sequence of a filtered chain complex over a field. Our method is based on a decomposition of the persistent homology. We demonstrate that, under fairly general…
We give a combinatorial classification of non-trivial triple Massey products of three dimensional classes in the cohomology of a moment-angle complex. This work improves on a result by Denham and Suciu (2007) by considering triple Massey…
We introduce and study configuration schemes, which are obtained by ``glueing'' usual schemes along closed embeddings. The category of coherent sheaves on a configuration scheme is investigated. Smooth configuration schemes provide…
We study the homotopy theory of polyhedral products associated to a combinatorial generalisation of manifolds known as pseudomanifolds. As special cases, we show that loop spaces of moment-angle manifolds associated to triangulations of…
Let M be a closed simply connected 2n-dimensional manifold. The present paper is concerned with the cohomology of classifying spaces of connected groups of homeomorphisms of M.
We prove that the factorization homologies of a scheme with coefficients in truncated polynomial algebras compute the cohomologies of its generalized configuration spaces. Using Koszul duality between commutative algebras and Lie algebras,…
We expand the toolbox of (co)homological methods in computational topology by applying the concept of persistence to sheaf cohomology. Since sheaves (of modules) combine topological information with algebraic information, they allow for…
Correlated rotational alignment spectroscopy correlates observables of ultrafast gas-phase spectroscopy with high-resolution, broad-band rotational Raman spectra. This article reviews the measurement principle of CRASY, existing…
In this paper, we define and prove basic properties of complement polyhedral product spaces, dual complexes and polyhedral join complexes. Then we compute the universal algebra of polyhedral join complexes under certain split conditions and…
The purpose of this article is to relate coarse cohomology of metric spaces with a more computable cohomology. We introduce a notion of boundedly supported cohomology and prove that coarse cohomology of many spaces are isomorphic to the…
Let us say that a map of arcwise connected topological spaces (having the homotopy type of CW-complexes) is a pseudo-homeomorphism if it induces an isomorphism of the first integer homology groups and an epimorphism of the second integer…
Replacing configurations of points by configurations of tubular neighbourhoods (or discs) in a manifold, we are able to define a natural scanning map that is equivariant under the action of the diffeomorphism group of the manifold. We also…
We study cosmological perturbations in the context of an interacting dark energy model, in which the cosmological term decays linearly with the Hubble parameter, with concomitant matter production. A previous joint analysis of the…
Using the technique of quasi difference sets we characterize geometry and automorphisms of configurations which can be presented as a join of some others, in particular - which can be presented as series of cyclically inscribed copies of…
We study measures on the configuration spaces of two type particles. Gibbs measures on the such spaces are described. Main properties of corresponding relative energies densities and correlation functions are considered. In particular, we…
Smooth parametrization consists in a subdivision of the mathematical objects under consideration into simple pieces, and then parametric representation of each piece, while keeping control of high order derivatives. The main goal of the…
It is shown that a surjective monotone map $X\to Y$ between finite $T_0$-spaces induces a surjective map on homology. As such a map turns out to be a sequence of edge contractions in the Hasse diagram of $X$, followed by a homeomorphism,…
Symmetric products of curves are important spaces for both geometers and topologists, and increasingly useful objects for physicists. We summarize in this note some of their basic homotopy theoretic properties and derive a handful of known…